The Inter man started his country's opening group match against Ecuador but was substituted late on in the 4-0 victory.
Vecino complained of pain in his thigh and scans have subsequently revealed an injury that will keep him out of the rest of the tournament.
Star Uruguay forwards Luis Suarez and Edinson Cavani each suffered with issues earlier this year but both scored in the convincing win.
Head coach Oscar Tabarez has options to replace Vecino in midfield, with Gaston Pereiro, Lucas Torreira and Federico Valverde all appearing from the bench against Ecuador.
Uruguay play Japan in their second match on Thursday before taking on Chile at the start of next week.
Former Fiorentina man Vecino made 30 appearances in Serie A in 2018-19, scoring three times as Inter finished fourth.